A device is known so far which is constructed such that the output torque of the engine is transmitted to the transmission through the torque converter (hereafter, “tor-con”) (for instance, refer to Patent Document 1). The device described in this Patent Document 1 calculates a speed ratio, which is a ratio of rotational speeds on an input axis side and an output axis side of the tor-con, and performs an upshift or a downshift of the speed stage, when the ratio of the rotational speeds reaches a predetermined value set beforehand.    [Patent Document 1] Japanese Patent No. 3388594